{"id":"https://openalex.org/W7225200916","doi":"https://doi.org/10.5281/zenodo.23924544","title":"An Equivariance Principle for the Axiomatic Method","display_name":"An Equivariance Principle for the Axiomatic Method","publication_year":2026,"publication_date":"2026-11-03","ids":{"openalex":"https://openalex.org/W7225200916","doi":"https://doi.org/10.5281/zenodo.23924544"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.23924544","doi":"https://doi.org/10.5281/zenodo.23924544","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23924544","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"volume":null,"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.23924544","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5160488356","display_name":"Frank Feys","orcid":"https://orcid.org/0009-0000-7667-6742","observed_orcids":["https://orcid.org/0009-0000-7667-6742"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Feys, Frank","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0009-0000-7667-6742","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5160488356"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10991","display_name":"Game Theory and Voting Systems","score":0.9160000085830688,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10991","display_name":"Game Theory and Voting Systems","score":0.9160000085830688,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.02280000038444996,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.013000000268220901,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/axiomatic-method","display_name":"axiomatic method","score":0.8009999990463257},{"id":"https://openalex.org/keywords/group-actions","display_name":"group actions","score":0.7559999823570251},{"id":"https://openalex.org/keywords/fixed-sets","display_name":"fixed sets","score":0.6420000195503235},{"id":"https://openalex.org/keywords/stabilizers","display_name":"stabilizers","score":0.5950000286102295},{"id":"https://openalex.org/keywords/may-s-theorem","display_name":"May's theorem","score":0.8970000147819519},{"id":"https://openalex.org/keywords/nash-bargaining","display_name":"Nash bargaining","score":0.9789999723434448},{"id":"https://openalex.org/keywords/shapley-value","display_name":"Shapley value","score":1.0}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7904999852180481},{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.6348999738693237},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.5769000053405762},{"id":"https://openalex.org/C125773388","wikidata":"https://www.wikidata.org/wiki/Q792542","display_name":"Axiomatic system","level":3,"score":0.4643999934196472},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.4350999891757965},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.41530001163482666},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.38769999146461487},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38760000467300415},{"id":"https://openalex.org/C171036898","wikidata":"https://www.wikidata.org/wiki/Q256355","display_name":"Equivariant map","level":2,"score":0.38449999690055847},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3407999873161316},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.32420000433921814},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3199000060558319},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.31310001015663147},{"id":"https://openalex.org/C100643331","wikidata":"https://www.wikidata.org/wiki/Q205170","display_name":"Power set","level":3,"score":0.304500013589859},{"id":"https://openalex.org/C137212723","wikidata":"https://www.wikidata.org/wiki/Q1948412","display_name":"Morphism","level":2,"score":0.29580000042915344},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.29490000009536743},{"id":"https://openalex.org/C154690210","wikidata":"https://www.wikidata.org/wiki/Q1668499","display_name":"Rewriting","level":2,"score":0.28690001368522644},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.2840999960899353},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.27720001339912415},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.27480000257492065},{"id":"https://openalex.org/C117354338","wikidata":"https://www.wikidata.org/wiki/Q1165112","display_name":"Singleton","level":3,"score":0.2630000114440918},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.2567000091075897},{"id":"https://openalex.org/C58193220","wikidata":"https://www.wikidata.org/wiki/Q1778193","display_name":"Direct product","level":2,"score":0.25529998540878296},{"id":"https://openalex.org/C74497983","wikidata":"https://www.wikidata.org/wiki/Q1330788","display_name":"Weierstrass factorization theorem","level":3,"score":0.2547000050544739},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.2522999942302704},{"id":"https://openalex.org/C160343418","wikidata":"https://www.wikidata.org/wiki/Q185256","display_name":"Rigidity (electromagnetism)","level":2,"score":0.25209999084472656}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.23924544","doi":"https://doi.org/10.5281/zenodo.23924544","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23924544","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.5281/zenodo.23924545","doi":"https://doi.org/10.5281/zenodo.23924545","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23924545","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.5281/zenodo.23924544","doi":"https://doi.org/10.5281/zenodo.23924544","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23924544","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7225168319","https://openalex.org/W1994685906","https://openalex.org/W2077812506","https://openalex.org/W1580996432","https://openalex.org/W2023740769","https://openalex.org/W6991229671","https://openalex.org/W2026063038","https://openalex.org/W2023481519","https://openalex.org/W2041699933","https://openalex.org/W6960376452"],"abstract_inverted_index":{"A":[0],"G-equivariant":[1],"map":[2],"R:":[3],"X":[4],"\u2192":[5],"T":[6],"must":[7],"send":[8],"each":[9],"x":[10],"into":[11],"Fix_T(Stab_G(x));":[12],"the":[13,22,68,74,78,95,98,102,112],"set":[14],"of":[15,27,59,77],"all":[16],"such":[17],"maps":[18],"bijects":[19],"naturally":[20],"with":[21,85],"product":[23,84],"over":[24],"orbit":[25],"representatives":[26],"Fix_T(Stab_G(x)).":[28],"An":[29],"empty":[30],"factor":[31,40],"is":[32,36,114],"impossibility,":[33,100],"a":[34,38,42,56,118],"singleton":[35],"characterization,":[37],"larger":[39],"parametrizes":[41],"family.":[43],"The":[44],"bijection":[45],"has":[46],"been":[47],"folklore":[48],"since":[49],"Eckmann":[50],"(1954).":[51],"We":[52],"build":[53],"on":[54],"it":[55],"rigidity":[57],"taxonomy":[58],"output":[60],"spaces":[61],"and":[62,101,111],"an":[63],"additive":[64],"refinement":[65],"theorem":[66,104],"via":[67],"coinvariant":[69],"Grothendieck":[70],"group":[71],"(X^gp)_G,":[72],"exhibiting":[73],"impossibility-characterization":[75],"dichotomy":[76],"axiomatic":[79],"corpus":[80],"as":[81],"one":[82],"fixed-set":[83],"three":[86],"regimes.":[87],"Five":[88],"classical":[89],"results":[90],"(May's":[91],"theorem,":[92],"Nash":[93],"bargaining,":[94],"Shapley":[96],"value,":[97],"anonymity-neutrality-resoluteness":[99],"constraint":[103],"for":[105],"label-symmetric":[106],"classification)":[107],"are":[108],"derived":[109],"uniformly,":[110],"recipe":[113],"applied":[115],"cold":[116],"to":[117],"novel":[119],"problem.":[120]},"counts_by_year":[],"updated_date":"2026-11-05T12:25:35.769452","created_date":"2026-11-04T00:00:00"}